Deck 3: Describing Data: Numerical Measures

Question 1

According to Chebyshev's theorem, 75% of the observations lie within plus and minus 2.00 average mean deviations.

Answer 1

False

Question 2

The variance is the mean of the sum of the squared deviations between each observation and the median.

Answer 2

False

Question 3

According to the Empirical rule, about 95% of the observations lie within plus and minus 2.00 standard deviations.

Answer 3

True

Question 4

In a company, the standard deviation of the ages of female employees is 6 years and the standard deviation of the ages of male employees is 10 years. These statistics indicate that the dispersion of age is greater for females than for males.

Question 5

Which measures of central location are not affected by extremely small or extremely large values?

A) Mean and median
B) Mean and mode
C) Mode and median
D) Standard deviation and mean

Question 6

For any data set, Chebyshev's theorem estimates the proportion of observations that occurs within k standard deviations of the mean, where k is greater than 1.0.

Question 7

The sum of the deviations from the mean for the set of numbers 4, 9, and 5 will equal zero.

Question 8

The sum of the deviations of each data value from this measure of central location will always be zero.

A) Mode
B) Mean
C) Median
D) Standard deviation

Question 9

Variation describes the degree of dispersion in the data.

Question 10

The standard deviation is the positive square root of the variance.

Question 11

A set of ordinal-, interval-, or ratio-level data may only have one mode.

Question 12

For any data set, which measures of central location have only one value?

A) Mode and median
B) Mode and mean
C) Mode and standard deviation
D) Mean and median

Question 13

For a set of data arranged or sorted in numerical order, the value of the observation in the center is called the weighted mean.

Question 14

In a sample of 10 people, 3 persons earn $8 an hour, 6 earn $9 an hour, and 1 earns $12 an hour. The weighted mean hourly wage is $9.

Question 15

The geometric mean is the n^th root of n observations.

Question 16

The arithmetic mean is the sum of the quantitative observations divided by the total number of observations.

Question 17

For any distribution, there are an equal number of values above and below the mean.

Question 18

The mode is the value of the observation that appears most frequently.

Question 19

Extremely high or low scores affect the value of the median.

Question 20

A value that is typical or representative of the data is referred to as a measure of central location.

Question 21

For a data set with an odd number of observations that have been sorted from smallest to largest values, where is the median located?

A) n
B) n/2
C) (n + 1)/2
D) n + ½

Question 22

What is the relationship among the mean, median, and mode in a symmetric distribution?

A) They are all equal.
B) The mean is always the smallest value.
C) The mean is always the largest value.
D) The mode is the largest value.

Question 23

Which one of the following is referred to as the population mean?

A) µ
B) s
C) σ
D) χ

Question 24

The times (in minutes) that several underwriters took to review applications for similar insurance coverage are 50, 230, 52, and 57. What is the median length of time required to review an application?

A) 54.5
B) 141.0
C) 97.25
D) 109.0

Question 25

A sample of the paramedical fees charged by clinics revealed these amounts: $55, $49, $50, $45, $52, and $55. What is the median charge?

A) $47.50
B) $51.00
C) $52.00
D) $55.00

Question 26

A question in a market survey asks for a respondent's favorite car color. Which measure of central location should be used to summarize this question?

A) Mode
B) Median
C) Mean
D) Standard deviation

Question 27

A stockbroker placed the following order for a customer: • 50 shares of Kaiser Aluminum at $104 a share
• 100 shares of GTE at $25.25 a share
• 20 shares of Boston Edison at $9.125 a share
What is the weighted arithmetic mean price per share?

A) $25.25
B) $79.75
C) $103.50
D) $46.51

Question 28

A sample of single persons receiving Social Security payments revealed these monthly benefits: $826, $699, $1,087, $880, $839, and $965. How many observations are below the median?

A) 1
B) 2
C) 3
D) 3.5

Question 29

What is the median of 26, 30, 24, 32, 32, 31, 27, and 29?

A) 32
B) 29
C) 30
D) 29.5

Question 30

Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as __________.

A) Symmetric
B) Bimodal (having two modes)
C) Positively skewed
D) Negatively skewed

Question 31

For a data set, half of the observations are always greater than the ____.

A) Median
B) Mode
C) Mean
D) Standard deviation

Question 32

What is the lowest level of measurement to which a median can be computed?

A) Nominal
B) Ordinal
C) Interval
D) Ratio

Question 33

A bottling company offers three kinds of delivery service: instant, same day, and within five days. The profit per delivery varies according to the kind of delivery. The profit for an instant delivery is less than the other kinds because the driver has to go directly to a grocery store with a small load and return to the bottling plant. To find out what effect each type of delivery has on the profit picture, the company summarized the data in the following table based on deliveries for the previous quarter. What is the weighted mean profit per delivery?

A) $72
B) $110
C) $142
D) $97

Question 34

Assume a student received the following grades for the semester: History, B; Statistics, A; Spanish, C; and English,C. History and English are 5 credit-hour courses, Statistics a 4 credit-hour course, and Spanish is a 3 credit-hour course. If 4 grade points are assigned for an A, 3 for a B, and 2 for a C, what is the weighted mean grade for the semester?

A) 4.00
B) 1.96
C) 2.76
D)
3)01

Question 35

A survey item asked students to indicate their class in college: freshman, sophomore, junior, or senior. Which measure(s) of central location would be appropriate for the data generated by that questionnaire item?

A) Mean and median
B) Mean and mode
C) Mode and median
D) Mode only

Question 36

For the most recent seven years, the U.S. Department of Education reported the following number of bachelor's degrees awarded in computer science: 4,033; 5,652; 6,407; 7,201; 8,719; 11,154; 15,121. What is the annual arithmetic mean number of degrees awarded?

A) About 12,240
B) About 8,327
C) About 6,217
D) About 15,962

Question 37

The net incomes (in $millions) of a sample of steel fabricators are $86, $67, $86, and $85. What is the modal net income?

A) $67
B) $85
C) $85.5
D) $86

Question 38

On a finance exam, 15 accounting majors had an average grade of 90. On the same exam, 7 marketing majors averaged 85, and 10 finance majors averaged 93. What is the weighted mean for all 32 students taking the exam?

A) 89.84
B) 89.33
C) 89.48
D) 10.67

Question 39

Over the last six months, the following numbers of absences have been reported: 6, 0, 10, 14, 8, and 0. What is the median number of monthly absences?

A) 6
B) 7
C) 8
D) 3

Question 40

During the past six months, a purchasing agent placed the following three orders for coal: What is the weighted arithmetic mean price per ton?

A) $87.25
B) $72.33
C) $68.47
D) $89.18

Question 41

A population consists of all the weights of all defensive tackles on a university's football team. They are Johnson, 204 pounds; Patrick, 215 pounds; Junior, 207 pounds; Kendron, 212 pounds; Nicko, 214 pounds; and Cochran, 208 pounds. What is the population standard deviation (in pounds)?

A) About 4
B) About 16
C) About 100
D) About 40

Question 42

What is the relationship between the variance and the standard deviation?

A) Variance is the square root of the standard deviation.
B) Variance is the square of the standard deviation.
C) Variance is twice the standard deviation.
D) There is no constant relationship between the variance and the standard deviation.

Question 43

A purchasing agent for a trucking company is shopping for replacement tires for their trucks from two suppliers. The suppliers' prices are the same. However, Supplier A's tires have an average life of 60,000 miles with a standard deviation of 10,000 miles. Supplier B's tires have an average life of 60,000 miles with a standard deviation of 2,000 miles. Which of the following statements is true?

A) The two distributions of tire life are the same.
B) On average, Supplier A's tires have a longer life than Supplier B's tires.
C) The life of Supplier B's tire is more predictable than the life of Supplier A's tires.
D)
The dispersion of Supplier A's tire life is less than the dispersion of Supplier B's tire life.
The tire life for Supplier B is more predictable because the standard deviation of the tire life is smaller for Supplier B than SupplierA.

Question 44

The distribution of a sample of the outside diameters of PVC pipes approximates a symmetrical, bell-shaped distribution. The arithmetic mean is 14.0 inches, and the standard deviation is 0.1 inches. About 68% of the outside diameters lie between what two amounts?

A) 13.5 and 14.5 inches
B) 13.0 and 15.0 inches
C) 13.9 and 14.1 inches
D) 13.8 and 14.2 inches

Question 45

The sample variance of hourly wages was 10. What is the sample standard deviation?

A) $1.96
B) $4.67
C) $3.16
D) $10.00

Question 46

For a sample of similar sized all-electric homes, the March electric bills were (to the nearest dollar): $212, $191, $176, $129, $106, $92, $108, $109, $103, $121, $175, and $194. What is the range?

A) $100
B) $130
C) $120
D) $112

Question 47

For the past week, a company's common stock closed with the following prices: $61.5, $62, $61.25, $60.875, and $61.5. What was the price range?

A) $1.250
B) $1.750
C) $1.125
D) $1.875

Question 48

The ages of all the patients in the isolation ward of the hospital are 38, 26, 13, 41, and 22. What is the population variance?

A) 106.8
B) 91.4
C) 240.3
D) 42.4

Question 49

A sample of wires coming off the production line was tested for tensile strength. The statistical results (in PSI) were the following: According to the Empirical rule, the middle 95% of the wires tested had a tensile strength between approximately what two values?

A) 450 and 550
B) 460 and 540
C) 420 and 580
D) 380 and 620

Question 50

The following are the weekly amounts of welfare payments made by the federal government to a sample of six families: $139, $136, $130, $136, $147, and $136. What is the range?

A) $0
B) $14
C) $52
D) $17

Question 51

A sample of small bottles and their contents has the following weights (in grams): 4, 2, 5, 4, 5, 2, and 6. What is the sample variance of bottle weight?

A) 6.92
B) 4.80
C) 1.96
D) 2.33

Question 52

A disadvantage of using an arithmetic mean to summarize a set of data is that __________.

A) The arithmetic mean sometimes has two values
B) It can be used for interval and ratio data
C) It is always different from the median
D) It can be biased by one or two extremely small or large values

Question 53

What is a disadvantage of the range as a measure of dispersion?

A) It is based on only two observations.
B) It can be distorted by a large mean.
C) It is not in the same units as the original data.
D) It has no disadvantage.

Question 54

If the variance of the "number of daily parking tickets issued is 100, the standard deviation is defined as the _____________.

A) "Number of daily parking tickets"
B) "Number of daily parking tickets" squared
C) Absolute value of the variance of the "number of daily parking tickets"
D) Square root of the variance of the "number of daily parking tickets"

Question 55

A sample of assistant professors on the business faculty at state-supported institutions in Ohio revealed the mean income to be $72,000 for nine months, with a standard deviation of $3,000. Using Chebyshev's theorem, what proportion of the faculty earns more than $66,000, but less than $78,000?

A) At least 50%
B) At least 25%
C) At least 75%
D) At least 100%

Question 56

The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. The sample mean is $150 and the standard deviation is $20. Using the Empirical rule, about 95% of the monthly food expenditures are between what two amounts?

A) $100 and $200
B) $85 and $105
C) $205 and $220
D) $110 and $190

Question 57

The sum of the differences between sample observations and the sample mean is equal to _______.

A) Zero
B) The mean deviation
C) The range
D) The standard deviation

Question 58

Based on the Empirical rule, what percent of the observations will lie between plus or minus two standard deviations from the mean?

A) 95%
B) 5%
C) 68%
D) 2.5%

Question 59

The mean, as a measure of central location, would be inappropriate for which one of the following?

A) Ages of adults at a senior citizen center
B) Incomes of lawyers
C) Number of pages in textbooks on statistics
D) Marital status of college students at a particular university

Question 60

According to Chebyshev's theorem, at least what percent of the observations lie within plus and minus 1.75 standard deviations of the mean?

A) 56%
B) 95%
C) 67%
D) 100%

Question 61

In a frequency distribution, the class with the largest number of observations is called the ___________.

Question 62

The measure of central location that requires the data to be ranked before it is possible to determine it is called the _________.

Question 63

Which measure of central location is used to determine an average annual percent increase?

A) Arithmetic mean
B) Weighted mean
C) Mode
D) Geometric mean

Question 64

The number of students at a local university increased from 2,500 students to 5,000 students in 10 years. Based on a geometric mean, the university grew at an average percentage rate of

A) 2,500 students per year.
B) 1.071 percent per year.
C) 7.1 percent per year.
D) 250 students per year.

Question 65

The net annual sales of a sample of small retail clothing stores were organized into the following relative frequency distribution. What is the mean net sales (in $ millions)?

A) $7.09
B) $10.09
C) $8.59
D) Mean cannot be computeD.

Question 66

The measure of central location that uses all of the observations in its calculation is called the ___________.

Question 67

A statistic computed by summing all of the values of a distribution and dividing by the number of values is called the __________.

Question 68

Each person who applies for an assembly job at Robert's Electronics is given a mechanical aptitude test. One part of the test involves assembling a plug-in unit based on numbered instructions. A sample of the length of time it took 42 persons to assemble the unit was organized into the following frequency distribution. What is the standard deviation (in minutes)?

A) 3.89
B) 6.01
C) 8.78
D) 17.00

Question 69

If a distribution is highly skewed, the measure of central location called the ________ should be avoided.

Question 70

The Investment Research Institute reported in its Mutual Fund Fact Book that the number of mutual funds increased from 5725 in 1999 to 7977 in 2009. What is the geometric mean annual percent increase in the number of funds?

A) 1.034
B) 3.37
C) 39.34
D) 71.11
E) 633.5

Question 71

The variance of a sample of 121 observations equals 441. The standard deviation of the sample equals

A) 11.
B) 21.
C) 1.91.
D) 231.

Question 72

If a set of quantitative observations contains an extreme value, the most representative measure of central location would be the __________.

Question 73

The U.S. Federal Aviation Administration reported that passenger revenues on international flights increased from $528 million in 1986 to $5,100 million in 2009. What is the geometric mean annual percent increase in international passenger revenues?

A) 10.4
B) 27.9
C) 103.6
D) 9.96

Question 74

The weekly sales from a sample of 10 computer stores yielded a mean of $25,900, a median of $25,000, and a mode of $24,500. Given this, the shape of the distribution would be _________.

Question 75

Consider two populations with the same mean. Since they have the same mean, then:

A) Their standard deviations must also be the same.
B) Their medians must also be the same.
C) Their modes must also be the same.
D) None of these is correct.

Question 76

The same mean:

A) Is always equal to the population mean.
B) Is always smaller than the population mean.
C) Is found by adding the data values and dividing them by (n-1).
D) Is found by adding all data values and dividing them by n.

Question 77

Production of passenger cars in Japan increased from 3.94 million in 1999 to 6.74 million in 2009. What is the geometric mean annual percent increase?

A) 4.0
B) 1.9
C) 5.5
D) 16.6
E) 47.3

Question 78

The value that occurs most often in a set of data is called the ________.

Question 79

In the calculation of the arithmetic mean for grouped data, which value is used to represent all the values in a particular class?

A) The upper limit of the class.
B) The lower limit of the class.
C) The frequency of the class.
D) The cumulative frequency preceding the class.
E) The class midpoint.

Question 80

When computing the mean, the smallest value

A) can never be negative.
B) can never be zero.
C) can never be less than the mean.
D) can be any value.